I. Field of the Invention
This invention relates to a method of reducing the amount of uncertainty in a terrain referenced navigation system while flying over water, flat ground or shifting desert and dunes and more particularly to a method of correlating electromagnetic and gravimetric information relative to the flight path of an aircraft under direction of a terrain referenced navigation system.
II. Background of Terrain Referenced Navigation
One prior art terrain aided navigation system is available from Sandia Labs. Sandia has created the Sandia Inertial Terrain-Aided Navigation (SITAN) flight-computer algorithm that produces a very accurate trajectory for low-flying, high-performance aircraft by combining outputs from a radar or laser altimeter, an inertial navigation system (INS), and a digital terrain elevation map. SITAN is a recursive, real time, terrain-aided navigation algorithm for use on fighter aircraft. The algorithm has been implemented in a popular microprocessor. The aircraft's position can be estimated within a 926 meter circle error of probability. A good description of the SITAN terrain aided navigation system can be found in the proceedings of the IEEE National Aerospace and Electronics Conference--NAECON, May 20-24, 1985 entitled The AFTI/F16 Terrain-Aided Navigation System, by D. D. Boozer, M. K. Lau, J. R. Fellerhoff, Sandia National Laboratories, Albuquerque, N. Mex. 87185.
SITAN utilizes Kalman filter algorithms to process geophysical measurements. The algorithm estimates errors in a flight path produced by an inertial navigation system following the equations given in the above-mentioned article quoted below.
"The Kalman filter can be formed with the following state model and measurement: ##EQU1## wherein: .delta.X.sub.k =INS error states to be estimated PA0 Since the measurement function c(x) is a nonlinear function of the states, the standard extended Kalman filter approach is used to obtain the measurement matrix, ##EQU2## where h.sub.x and h.sub.y are the terrain slopes in the x and y directions of the map evaluated at X.sub.k (-), the predicted aircraft position just before a measurement is processed at time k. The first three states are taken to be the x position, y position, and altitude, respectively. At any time k, EQU X=X.sub.INS +.delta.X PA0 The state vector often used in a single filter implementation is EQU .delta.X=[.delta.X .delta.Y .delta.Z .delta.V.sub.x .delta.V.sub.y ].sup.T PA0 where .delta.X, .delta.Y, .delta.Z, .delta.V.sub.x, and .delta.V.sub.Y are errors in the X position, Y position, altitude, X velocity, and Y velocity, respectively. Other INS errors and states can also be included in .delta.X by using the proper .phi.. PA0 Parallel SITAN was developed because the distance needed by SITAN to reach steady state becomes excessive as initial position errors (IPEs) approach several hundred meters. Parallel SITAN is a bank of extended Kalman filters that process identical altimeter measurements. After some updates, the filter with the minimum average weighted residual squared (AWRS) value is identified as having the correct position estimate. The AWRS value is defined by ##EQU3## where .DELTA..sub.i is the residual at ith update, n is the number of updates, and HPH.sup.T +R is the residual variance. Once the IPEs are reduced by the parallel filters, a single filter performs well, starting off essentially in steady state. PA0 To implement parallel SITAN, the number and geometrical layout of the parallel filters needed to cover an IPE must be specified. A square, constant-spaced grid can be used to center the filters about the horizontal position indicated by the INS. Filters at and near the corners are then eliminated to reduce the number of filters. To further lighten the computational burden, three-state, instead of five-state, filters are often used in parallel SITAN with EQU .delta.X=[.delta.X .delta.Y .delta.Z].sup.T PA0 For both the single and parallel filter implementation's least-squares plane fit to the map, known as stochastic linearization, is used to compute the slopes, h.sub.X and H.sub.Y. Horizontal uncertainties .sigma..sub.X and .sigma..sub.Y from the error-covariance matrix, defined by and are used to determine the size of the plane. Residuals ##EQU4## from the plane fit, RFIT.sub.k, are added to the measurement error variance, R.sub.k, to ensure that the SITAN filter assigns less weight to the measurement when the plane fit is either very large or is over a rough area, thus adapting to local terrain." PA0 With the design for the acquisition, lost, and track modes as described above, the mode-control logic (FIG. 6) is needed to determine in which mode the algorithm should operate. When large aircraft position errors exist, it should choose the acquisition mode; with small errors, the track. The main parameter used in the mode-control logic for transition from acquisition to track is the AWRS. FIG. 7 shows a cross-section of a three-dimensional AWRS surface where AWRS is a function of the parallel filter positions (X.sub.j, Y.sub.j). In the acquisition mode the parallel filters will tend to migrate to the relative minima of this surface. PA0 To keep the parallel filters from migrating too far from their initial positions, a maximum of 128 updates is allowed. Four tests are performed after every 32 updates to determine if transition to the track mode is possible by selecting the acquisition filter with the minimum AWRS. Test 1 requires the selected filter to have an AWRS lower than a threshold value to ensure that the parallel filters are indeed over the correct aircraft position. If the parallel filters are configured over an area which does not include the true aircraft position, the global minimum of the AWRS curve is expected to shift upward. Test 2 requires contrast in the terrain, a sufficient different between AWRS.sub.min and AWRS.sub.max to prevent transition to the track mode over very smooth areas such as water. Test 3, the false-fix test, requires that the minimum AWRS outside of an exclusion region, AWRS*.sub.min does not compete with AWRS.sub.min, where the size of the exclusive region is computed using .sigma..sub.x and .sigma..sub.Y of the selected filter. Statistically, as more updates are made, the separation between the global minimum and relative minima can be realized and still retain the same confidence level. Therefore, the required separation between AWRS*.sub.min and AWRS.sub.min should be a function of 1/n, where n is the number of updates. Test 4 requires the .sigma..sub.X and .sigma..sub.Y of the selected filter to be smaller than its initial value, 200 m, indicating that improvements have been made in estimating the aircraft's position during acquisition.
.phi.=state-transition matrix for INS errors PA1 X.sub.k =states of INS and aircraft PA1 C.sub.k =ground clearance measurement PA1 Z.sub.k =altitude of aircraft PA1 h=height of terrain at position ( .,. ) PA1 W.sub.k =driving noise with E(W.sub.k)=0 for all k and E(W.sub.k W.sub.j.sup.T)=Q.sub.k .delta.kj PA1 V.sub.k =measurement error With E(V.sub.k)=0 for all k and E(V.sub.k V.sub.j)=R.sub.k .delta..sub.kj PA1 k=Subscript denoting time k.
SITAN has three basic modes: acquisition mode, lost mode and track mode.